Hungary - Math Olympiad Question

Easiest one ever!!

[petrmatejka]

you can also split it to prime numbers - you will have 2^20 x 5^20 / (2^20 x 5^10).
2^20 will cancel, and division rule gives you 5^10

[natalmi]

Seems like everyone in this comment section is a genius. If you think this is too easy for you, you're obviously not the target audience for this video. Just appreciate that there are people who have the willingness and kindness to set apart some of their own personal time to teach other people.

[yc]

I sincerely hope this wasn’t a math Olympiad question!

[HarishKini]

The easiest way to solve this is to write the numerator 10^20 as 100^10. And now since bot N and D is raised to 10, you can combine it as 100/5=20 raised to 10

[RudySchmidt-ic]

I am noticing a sloppiness with mathematical language. For example the instruction given is "solve" when the correct instruction should be "evaluate". Solve seems to be used now as a universal term meaning to find the answer. Used correctly in mathematics it is used when dealing with equations ir triangles. Also people are using the word "power" when the term "exponent" is needed. The term "power" refers to a term having a base and an exponent. For example "2 squared" is a power
having an exponent of 2. Over my years of teaching mathematics I have learned that mathematics is a language and it is very important to use its vocabulary correctly. Sloppiness is a bad habit with any language but in particular with mathematics.

[scmtuk]

Generally, where you have (x^y)/(y^x), you can substitute y for ax, where a is the proportion between x and y, for example, in this video, a = 2. This makes it so that there's only one unknown variable (the variable "a" would obviously already be known)
This then becomes (x^ax) /((ax)^x), which then becomes x^(ax - x) / (a^x)
If we then substitute ax back for y, you get x^(y - x) / (y/x)^x
And this just simplifies back as (x^y)/(y^x), if anyone cares.

Anyway, if we plug in the values x = 10, and y = 20, we get:

10^(20 - 10) / (20/10)^10
This simplifies to 10^10 / 2^10
This then becomes (10/2)^10
Which then becomes 5^10
Which of course, becomes 9, 765, 625.

[aniket]

It literally took me 5-10 secs in the head💀

[wjbq]

answer:5^10
shorten
10^20=(10^2)^10
(10^2/20)^10=(100/20)^10=5^10
excuse me!

[battle]

My initial approach was to take 10^20 / 20^10 and turn it into ( 2^0 x 10^20 ) / ( 2^10 x 10^10 ). Then I turned that into the two fractions 2^0 / 2^10 multiplied by ( 10^20 / 10^10 )
This ends you up with 10^10 / 2^10.

[igoretski]

2^10 is easier than 5^10, So the result could also be written as 10'000'000'000 / 1'024

[איילליבוביץ-בט]

a shorter answer: 10 to the power of 20 is 100 to the power of 10. then (100 divided by 20) to the power of 10. equals 5 to the power of 10

[HedelTorres]

thanks for these videos.. i did it in my head before opening it.. but thanks to your videos for reminding me all the way to do it..

[alscents]

10^20 / 20^10
= 10^10 / 2^10
= 5^10
= (5^5)^2

Powers of 5 (5, 25, 125, 625, 3125). So,

10^20 / 20^10 = (5^5)^2
= 3125^2
= (3000 + 125)^2
= 3000^2 + 2 * 3000 * 125 + 125^2
= 9, 000, 000 + 250 * 3000 + 3125 * 5
= 9, 000, 000 + 750, 000 + 3125 * (10 / 2)
= 9, 750, 000 + 31250 / 2
= 9, 750, 000 + 15, 625
= 9, 765, 625

[shachi]

Lil correction in math we use implies that in equation "=>" not while solving questions.

[tombufford]

Looks like a problem of commutative law and the exponential has a higher communative order. The problem is not very trivial.If 20 = A and B = 10 then A ^20/ B^10 and A cannot be simply divided by B. Well worth doing again !

[Gab]

You didn't really solve an equation as you said, you just simplified a mathematical expression.

[kennethkan]

10^20/20^10=?
20^10
=(10×2)^10
=(10^10)(2^10)
10^20/((10^10)(2^10))
=10^10/2^10
=(2×5)^10/2^10
=5^10

[Brid]

The way I used to solve this is:

Question is 10^20/20^10

Let's ignore the denominator for now and focus on simplifying the numerator first.
10^20 = 10^(2*10)
10^20 = (10^2)^10(using the rule (a^m)^n = a^(m*n)
10^20 = 100^10
10^20 = (5^10)*(20^10)[using the rule a^b * d^b = (ad)^b]
Now we place that part in place of 10^20 in the fraction.
(5^10)*(20^10)/(20^10)
On both numerator and denominator, we have 20^10. So, we can cancel them.
So, the final answer is 5^10.

[reinhardtristaneugen]

...I got as a result 5 multiplied by 10 to the power of 9... ...and my asymmetrics... ...it just sucks...
Le p'tit Daniel

[brnduljak]

I did everything in my mind. Funny Olympics in Hungary. For preschoolers?